Single Choice

The minimum acceleration with which a fireman can slide down a rope of breaking strength two-third of his weight is

AZero
B$$\dfrac {g}{3}$$
Correct Answer
C$$3g$$
D$$g$$

Solution

If fireman slides down with some acceleration then his apparent weight decreases. For critical condition rope can bear only $$\dfrac {2}{3}$$rd of the fireman's weight. Let $$a$$ is the minimum acceleration then,
Tension in the rope $$= m(g - a) =$$ Breaking strength
$$\Rightarrow m (g - a) = \dfrac {2}{3} mg$$
$$\Rightarrow a = g - \dfrac {2g}{3} = \dfrac {g}{3}$$

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